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JEE Main 202522 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
22 January
Shift
Evening Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2025 · 22 January · Evening Shift · Physics · Units and Dimensions

Which one of the following is the correct dimensional formula for...

Which one of the following is the correct dimensional formula for the capacitance in F ? M,L,T\mathrm{M}, \mathrm{L}, \mathrm{T} and C stand for unit of mass, length, time and charge,

Options

  1. A[F]=[C2M−1 L−2 T2][\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]
  2. B[F]=[C2M−2 L2 T2][\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-2} \mathrm{~L}^2 \mathrm{~T}^2\right]
  3. C[F]=[CM−2 L−2 T−2][\mathrm{F}]=\left[\mathrm{CM}^{-2} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right]
  4. D[F]=[CM−1 L−2 T2][\mathrm{F}]=\left[\mathrm{CM}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]

Correct answer

A. [F]=[C2M−1 L−2 T2][\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]

Step-by-step solution

\begin{aligned} & \text{ Energy }=\frac{Q^2}{2 C} \\ & \begin{aligned} \therefore \quad[\mathrm{F}] & =\frac{\left[\mathrm{C}^2\right]}{\left[\mathrm{ML}^2 \mathrm{ T}^{-2}\right]} \\ & =\left[\mathrm{C}^2 \mathrm{M}^{-1} \mathrm{ L}^{-2} \mathrm{ T}^{+2}\right]\end{aligned}\end{aligned}$
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